As remarked in subsection:overview, the Hodge-theoretic results of
subsection:hodge-intro arise from an analysis of the Harder-Narasimhan filtrations of isomonodromic deformations of flat vector bundles on curves. Our first such result is a counterexample to
[1]},
[2]}, and
[3]}, which demonstrates that the situation is somewhat more complicated than was previously believed — there exist irreducible flat vector bundles whose isomonodromic deformations are never semistable.
